Depends on the OTA, if they don't provide the info at booking then I would not count on them providing it after booking either. Sometimes if you can find a link for the fare rules then you can see the booking code, but not always.

If it's a long enough flight that the miles matter then I'd just pay the extra $80 and book on Expedia where you can clearly see your booking class and know what you're getting. Or ring up the OTA you've found that's cheaper and ask them. If they don't know or won't say then I'd likely avoid them anyway.