The trick with any belt is to not make it too tight. I used the rubber mounts on an old Craftsman joiner, the original design was terrible so the machine vibrated like crazy.
I made a mount which hangs the motor, adjustable with a hand wheel. I used a much smaller Gates cogged belt than the original and even with that I found there was a narrow sweet spot at which the belt does not oscillate, definitely not too tight but also not too loose. I'm spinning the 3 knife cutter head at 5,500 RPM, the motor is 3,600 RPM, the motor balance is not great. The entire mount is supported by the bolts and bushings I pictured, I found a box of them when I went looking for something like that.
I used link belts on my mill drill and found the same thing but the sweet spots are much broader.
An idler pulley (or a roller like the serpentine belt tensioner on cars) on the slack side would be a good idea if possible, it's always the slack side that's a problem. If the lathe was mine I'd come up with a solution which has the motor mount horizontal rather than vertical, much easier to deal with and the rubber has a better chance of working.
You just have to watch the belts, it's easy to see.