I think I read somewhere that there are special configurations that can be made for a user application to request no battery optimizations, so that isn't surprising me.
Now about battery optimizations; in a lot of cases, it really won't make any difference. Basic applications that simply don't do any background processing won't change at all if subject to restrictions, or given free reign. I can't think of a single use for background processing on an authenticator application, so I really doubt it would make any difference.
Regarding the choice of application; many times, someone will tell you that you have to use "their" authenticator application, but when it really comes down to it, their application is just using regular run of the mill TOTP. Do you have access to the details? QR code? If it uses a QR code, you should try to just add it to a different TOTP program, like AndOTP.