When operating under their governor, they are paid by their governor. That’s why such a deployment would beg to be federally activated. DOD has a much bigger pot of money.
Feds can, and routinely do, pay for a wide variety of National Guard expenses while they are under State control (training, schooling, disaster response, etc.).
The accounts are already established and constantly exercised - just add money.
“such a deployment would beg to be federally activated. DOD has a much bigger pot of money.”
I think that this might be how this issue came up - Federal budget preparations, to potentially reimburse States. The budget is starting to shape up, and everyone is getting their placeholders in for the upcoming winnowing of priorities.
My understanding is that new funding for starting wall construction is expected in April (maybe May). It is possible that some Guard units might assist (SeaBees, or Engineers), stand guard (Infantry), or respond to riots/demonstrations (Military Police). Even if it is not part of the plan, it is a reasonable contingency preparation.