Any question answered...

I call it that too, but apparently it's Tbilisi now. I wonder when that change happened, my Russian lessons were in the 1980s. It was Tpilisi until 1936, and Tiflis to foreigners.

Well, according to Wikipedia the change happened in 1936:

Until 1936, the name of the city in English and most other languages was Tiflis, while the Georgian name was ტფილისი (Tpilisi).[8]

On 17 August 1936, by order of the Soviet leadership, the official Russian names of various cities were modified to more closely match the local language. In addition, the Georgian-language form T′⁠pilisi was modernized on the basis of a proposal by Georgian linguists; the ancient Georgian component ტფილი (tpili, "warm") was replaced by the newer თბილი (t′⁠bili).[8] This form was the basis for a new official Russian name (Тбилиси Tbilisi). Most other languages have subsequently adopted the new name form, but some language such as Turkish, Persian, Greek, and German have retained a variation of Tiflis.

https://en.wikipedia.org/wiki/Tbilisi

The reason appears to be the replacement of the older form of 'warm' with the newer one. From this article, it also seems that the name never was 'Tblisi'--that name doesn't even occur on the page. Perhaps it's a persistent spelling mistake, or the 'i' gets elided so people miss it, or it's a former Russian form?