Just a guess: your old Puch has straight wall rims. Yeah, blowing a high pressure tire off a straight wall rim isn't unheard of, and when it happens everybody will hear it. If you wanna run high pressure tires you'll be better off with hooked edge rims:
https://www.sheldonbrown.com/gloss_ho-z.html#hook
The other possibility is the tire wasn't seated correctly.
You'll do yourself favors to match the tire width to the rim width. Here's a chart:
https://www.sheldonbrown.com/tire-sizing.html#width