Is it true that ...

I have to measure trees that "shift into" a permanent sample plot?

If the center of a tree at DBH "moves into" a permanent plot over time, are you required to include it in the plot volume when it does so? No. You have a choice on this. The tree could move in because of unequal diameter growth or because the stem leaned that way.

If you put in a 1/5 acre plot in 1990, every tree in the area had the same chance of being included in the plot at that time. If a tree "leaned into" the plot when you returned in 1995, you can simply ignore it. Some people use the base of the tree to determine "in or out" to minimize this sort of problem, but it is not a problem at all. The same is true of trees that lean out of a PSP at a later date. You can continue to measure them.

Make sure you record the situation in the notes for the plot, so people know what you did and why. Tag the tree and note that it is "out" or at least reference it to two nearby trees in the plot so it can be identified.

Trees that were too small to be measured at the start of the process but were inside the plot will, of course, be added at a later date when they grow large enough to be included. That is a different problem altogether.

A valid general rule, therefore, is:

The position of the tree at the time of first measurement determines whether it will be measured for the entire time.

It is not wrong to have a different rule for trees which "move in and out of plots" (providing that you use the same rule for trees moving each way), but it adds to the variability that permanent plots try so hard to minimize. If the tree was in or out at the first measurement you can continue to treat it that way for the rest of the life of the PSP.