It is said on the webpage of AccentRPR that Rar 3.х is supported. Will the program work with archives created in WinRar 2.90?

Version format (RAR 3.x) but not the format of the archiver is specified in our description. Rar 3.x  format is now supported in WinRar 2.90 and is used in the current versions of WinRar ( 

So yes, the program runs with archives created in WinRAR 2.90 successfully.