Why would a C150 tachometer be sluggish?
No you don't have to "break in" flight instruments.

When a TSO'ed instrument is new it will get an Acceptance Test Procedure (a functional test) from the factory done before it is released and it has to perform to specification.  There is no such thing as a break in in service.

That being said, sometimes parts get by the ATP and malfunction in service, so you never know.  In my years in the regional airline industry, "bad from stock" is not uncommon even with super fancy Transport Category components.

Problems with the flex drive could be a factor, but a flex shaft would have to be binding and winding up a hell of a lot to create that kind of lag.  It's still something that could be checked.

Before that though, you should call Mitchell's tech support and describe what it's doing and see what they say.   Maybe they'll tell you there is a break in, but I'd be pretty surprised if they did.