More detailed data confirm the claim.
This chart is taken from https://ourworldindata.org/fossil-fuels ; most data there comes from the published paper:
Vaclav Smil (2017). Energy Transitions: Global and National Perspectives. & BP Statistical Review of World Energy..
It is coherent with figures from the World Bank: https://data.worldbank.org/indicator/EG.USE.COMM.FO.ZS ; https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE
The growth is indeed exponential or, arguably, linear since 1950 with a strong slope. The consumption reached 83,000 TWh in 1990, then 134,000 TWh in 2017.
Using data from the same source, the aggregated numbers confirm that 50% of total (1800-2017) consumption of fossil fuel has happened after 1990.
I basically summed the data in the online-available spreadsheet; I don't think that should be dismissed as "personal research" ?
edit: some comments debate whether fossil fuel consumption is the same as fossil fuel use (as per the OP). I cannot find easily whether the data here refers to the total primary energy of the fuel or to the energy produced after transformation - I strongly suspect it is the former, since it is much easier to compute (at any given time, there are several machines using coal, with different efficiency, so it is much easier to mesure the quantity of coal burned that the output). Moreover, the subtitle of the chart explicitely mentions primary energy. In case I am wrong, this chart should only be considered as a proxy for the question asked.