Quick summary:
- The first cases in Brazil were nearly 500km from the GM mosquito testing areas, the other side of a state larger than Spain
- Brazil wasn't even the first place this particularly explosive microcephaly-linked strain of the Asian lineage of Zika was spotted. Its genetics and behaviour link it to a very similar outbreak in French Polynesia (the other side of the Pacific Ocean) in 2013, which in turn is linked to a string of outbreaks in the South Pacific starting in Micronesia in 2007
- If going back in time and crossing the Pacific isn't challenging enough for even a GM mosquito, they'd have to have spontaneously changed sex, too. Zika, like all mosquito-borne diseases, is spread by female mosquitos. The GM mosquitos were all male (and infertile), and male mosquitos don't bite.
- Update March 2016: Evidence has been published in Science that Zika was present in Brasil between May and December 2013, well before the GM mosquito live-release field trials mentioned in the above claim.
In detail:
1. Did the 2015 outbreak of Zika center in a place where GMO mosquitoes were being tested?
Nope. The first cities with confirmed cases were Camaçari and Salvador, two cities on a peninsula just 40 km apart. They're nearly 500km or 6 hours 30 minutes by car from test site Juazeiro City. That's further apart than London and Frankfurt, or New York City and Ottawa. A long way for a mosquito that "cannot fly more than 400 meters".
They're in the same state - Bahia - but Brazilian states are big. Bahia is larger than Spain, for example. Camaçari and Salvador are near the coast, and the test grounds in and around Juazeiro are far inland, right on the Northern border between Bahia and Pernambuco.
Here's a map showing the distance involved. Salvador is on the tip of the peninsula just below the Camaçari marker, at the end of the yellow road visible in this image:

The complete locations of the GMO mosquito trial are:
some areas of the city of Juazeiro, northern state of Bahia, among them the Itaberaba district, and the districts of Mandacaru, Maniçoba and Carnaíba
(translation from Portuguese by Google, from the page of Moscamed, the Brazilian company working with Oxitec on the trial)
These locations are all in or near to Juazeiro. To resolve a possible source of confusion: the company sometimes refer to trials in "Itaberaba" conducted in both 2011 and 2014. There is a town, Itaberaba, visible on the above map, closer (but still not close) at around 100km from the first Zika hotspot, but this is not where they mean. A press release confirms that these trials were in "Itaberaba neighborhood of Juazeiro city", a suburb on the south eastern fringes of the city.
2. If so, does that mean that Oxitec's mission failed?
The GMO mosquitoes pilot tests were exactly that - tests, or as Oxitec put it:
extensive field trials
There's no reason to expect a field trial in one location to wipe out mosquitoes in another location hundreds of kilometers away.
Note that the trials were in specific districts of Juazeiro city. The trial wasn't expected to cover the whole of Juazeiro city, let alone the whole of a state larger than Spain.
Not only was the geographic scope of the trial very limited (as is perfectly normal for trials), it only targeted one of the two species of mosquito that are known to carry Zika: Aedes aegypti, and not Aedes albopictus.
3. Did Oxitec's mission in fact "backfire"?
Blaming these mosquito trials for the Zika outbreak is just silly. The GMO mosquitos would have to have changed sex, gone back in time at least one year, probably 7 years, then flown across the Pacific Ocean:
- The genetically modified mosquitoes released in the Brazil trial (OX513A) are male. Male mosquitoes don't bite, only female mosquitoes bite.
- This Zika outbreak follows the pattern of a less-reported 2013 outbreak in French Polynesia, in terms of phylogenetics of the virus, remarkable speed of spread, and correlation with upticks in microcephaly and Guillain–Barré. This outbreak in turn is linked to a 2007 outbreak in Micronesia which is the first recorded notable outbreak, and was long before the first release of OX513A mosquitos, in the caribbean Cayman Islands in 2009.
This remarkable strain of Zika didn't appear out of nowhere in Brazil.
Polynesia is the most likely origin for the Brazil outbreak, as outlined in this article in the journal Emerging Infectious Diseases:
Phylogenetic studies showed that the closest strain to the one that emerged in Brazil was isolated from samples from case-patients in French Polynesia and spread among the Pacific Islands (1); both strains belong to the Asian lineage. It has been assumed that ZIKV was introduced to Brazil during a World Cup soccer competition in 2014 (5), although no ZIKV-endemic Pacific countries competed. However, in August 2014, the Va’a World Sprint Championship canoe race was held in Rio de Janeiro, Brazil. Four Pacific countries (French Polynesia, New Caledonia, Cook Islands, and Easter Island) in which ZIKV circulated during 2014 had teams engaged in this contest in several categories
Rio is a very long way from Camaçari and Salvador, but Salvador was a venue for the July 2014 Brazil world cup.
Update March 2016: a paper has been published detailing evidence that Zika existed in Brazil before both events, between May and December 2013. These events therefore weren't the cause (though they might have contributed to the rapid spread across Brasil). From the abstract:
Phylogenetic and molecular clock analyses show a single introduction of ZIKV into the Americas, estimated to have occurred between May-Dec 2013, more than 12 months prior to the detection of ZIKV in Brazil. The estimated date of origin coincides with an increase in air passengers to Brazil from ZIKV endemic areas, and with reported outbreaks in Pacific Islands
As well as genetic similarity between the strains that spread in Brazil and the French Polynesia, there was also an increase in cases of both microcephaly and Guillain-Barré in French Polynesia, like that in Brazil; though it's worth noting that the microcephaly increase was small and wasn't noticed until researchers revisited the data after seeing events in Brazil.
WHO on Guillain-Barré and Zika in French Polynesia:
During the first outbreak of Zika from 2013 - 2014 in French Polynesia, which also coincided with an ongoing outbreak of dengue, national health authorities reported an unusual increase in Guillain-Barré syndrome
CDC on microcephaly and zika in French Polynesia:
...in French Polynesia where an outbreak occurred which involved more than 30,000 persons retrospectively after the Brazilian data became available - they went back and looked and saw an increase in microcephaly cases in their area
So it looks like nothing about this outbreak was seen for the first time in Brazil.
Note that, while the above article looks for a direct route for the virus from the South Pacific to Brazil, this is not necessarily necessary. Since Asian populations are known to have strong immunity to Asian strains of Zika like the one which arrived in Brazil, it could have come indirectly, via Asian travellers.