Word 2010 was the victim of an odd alteration by Microsoft: the AutoComplete tooltips work only for AutoText entries stored in the Normal.dotm template. I wasn't aware that using an entry in a table does work, but that's possibly just an oversight that complicated
the initial mistake. Microsoft corrected the behavior for later versions. (I assume that you know that Word 2010 is very long out of support, so there won't be any fixes for your computer unless you replace it with a current version.)
If your AutoText entries are stored in Building Blocks.dotx or some other template instead of Normal.dotm, you can move them to Normal.dotm -- although only one at a time. To do that, click Insert > Quick Parts > Building Block Organizer. Click the name
of an AutoText entry and click the Edit Properties button. In the Modify Building Block dialog, open the "Save in" dropdown and select Normal.dotm; then click OK.

You'll be prompted whether to redefine the building block entry; click Yes. Repeat this procedure for each remaining AutoText entry.
When you shut down Word you may get two prompts, one about saving the template that the entries were removed from, and one about saving Normal.dotm. Click Save in both prompts.