Yes - your rear tyre has failed internally through being run under-inflated, combined with the heat generated on the roller surface. As such that tyre is no longer suitable to ride on the road.
Indoor Trainers are hard on rear tyres - at least the ones that use a roller setup to interface resistance with the tyre.
There are roller-specific rear tyres available for this purpose, which have a much harder wearing surface, at the cost of grip. You would not use a trainer specific tyre on the road.
Or you can simply "use up" all those half-worn spare tyres that cyclists seem to acquire over time. I'd continue to use that tyre on a rear roller right through to where you can see cords, which is a lot deeper than I'd use on the road.