"Thanks so much, I'll let you know if I have any problems with it."
That's a seemingly normal enough comment. They want to get on with their day and you might also want the same. So you both say goodbye.
The problem, however, is that when it turns out there's a problem, you're likely busy, onto something else, or have forgotten the details that just transpired. So you either need to schedule another time to try to connect, and then recreate the issue, which may or may not be present when you are both ready.
Instead of the "easy" option of "I'll let you know if there are any issues", test it now. Before you part ways and end the visit. You may notice nothing, which is GREAT for the IT person because they can say "remember when we tested it and everything was working?" - that will help with your credibility.
And if you DO notice an issue, that's GREAT, too. Because you'll be able to resolve it there and then rather than find out only later that it's not working.
Test it now. Please. You're not done until they have tested it and see it working. Don't let their optimism of "I'm sure it's fine" distract you from the importance of a thorough job.