Since this problem could be major or minor, the first thing I would suggest is putting a vacuum gauge on it. This is easy to do, will reveal much, and unfortunately is a tool that many mechanics do not use.
If the manifold vacuum is not correct then a compression test should be run. If the compression is low on any cylinder then the valve lash should be inspected. If the valve lash is tight (especially with an exhaust valve) adjusting the lash may be a short term fix because a tight valve is often damaged. It will only get worse over time.
A vacuum gauge could also reveal whether or not there’s a vacuum leak. A vac. leak can cause this kind of symptom and an Idle Air Control valve problem can do the same.
From the sound of things these mechanics are skipping basic diagnostics and throwing parts at it.