I create short training videos on photoshop, I have the right to use material from the user's manual adobe referring to the source site?

Perhaps your answer would be found here: Copyright, Trademark and DMCA permissions | Adobe

To be truly safe, talk to your intellectual property attorney.

I really think you should run this by Adobe first.  I cannot comment about what you have done without seeing it.

My _opinion_ is that you would be OK so long as you reference the source.  If you passed the information off as your own, that would be different.