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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

fossil fuel consumption

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" ?