That's highly unlikely, to say the least. Can you post some images showing one of those glyphs in FontLab, and another from InDesign?
Some preliminary guesses: you changed the font but you didn't regenerate the font file; or, you have different versions of the same font; or, you have to clear your system font caches and those from InDesign, before an edited font is recognized.
Or you are comparing an Opentype alternative to its original.
(Either you are looking at the OTF alternative in FontLab, or you have some OTF feature switched on by default in InDesign.)
Or, it is remotely possible that you are looking at Priva One in Fontlab and Priva One Italic in InDesign, and you don't know that italic Cyrillic glyphs are supposed to be different from their (cough) Roman counterparts. Can you post a screenshot?