On Sat, 12 Sep 2015 15:34:11 -0400, John Somerset
wrote:

The hardware man said heat is used to slide PEX onto these fittings.
Rather than explain it, he gave me a piece of polybutylene.

He told you wrong. Heat is never used.

If I have to replace any more tubing, I want to use PEX. How do I slide
it on to a compression fitting designed for PEX and polybutylene? Is
heat the best way? Would a hair dryer be my best source? Would a
different brand of fitting solve the problem? Would faucet grease do
the trick?

No, not exactly.

Learn how to install PEX on a pipe stub out.
..