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Recommended levels doesn't mean you can't add tension to the setup. Does the turbo in question have a roll down test? My Computrainer had a range that it suggested. I'd normally do it up by feel (grabbing the wheel to see if it would slip when dragged over roller) and then do a roll down test after 10min warmup to double check and compensate for differing pressures.
I used a turbo-specific tyre briefly. It was such a ballache to fit that I basically never used it again after removing it. Easier to just use my normal road tyres. I use cheap, durable tyres for training so it's not much extra wear.
I've done that kind of thing before. I wouldn't say it's normal though. Check tyre pressure and tighten up the roller to tyre interface.