Clipping triode or ultralinear

Not all triode (or ultralinear) amps clip the same. It is the bi-product of clipping---high levels of ultrasonic garbage---that burns up tweeters. Different amps produce different amounts of that garbage when clipping, irrespective of class of operation.

Damaging a tweeter by clipping is far more common with underpowered solid state amps than tube!
Unless you can state that you fried the tweeter using a tube amp, I wouldn't worry about it, but to answer the question directly, the above responses are quite correct. If this is an on-going problem, I would consider installing a fuse to protect your tweeter, or consider a more powerful amp or a more efficient set of speakers so as to avoid clipping.

I have not had a problem for 39 years. Just wanted more information.
Thanks to everyone.

I don't think you need to change your listening habits if this is a problem that only happens once every 39 years or more ;-)

I must have PTSD. Post traumatic speaker disorder.