The inflationary expansion gradually decelerated. The change was not instantaneous, but “gradually” means over something like a billionth of a trillionth of a trillionth of a second!
In most inflationary models, the value of a scalar field filling all of space transitions from a nonzero value to a zero value as the field “rolls down its potential energy hill” to the bottom. The potential energy here is the energy of the field interacting with itself.
For example, a simple and classic model (but one no longer used in inflationary models) is the “Mexican hat” potential, $$V(\phi)=a(|\phi|^2-b^2)^2.$$ At high temperature, the field has the value 0 and the nonzero potential energy drives inflation. As the field evolves toward a value with $|\phi|=b$, the potential energy gradually drops to zero and inflation gradually stops.
Update to new questions posed by OP on 1/29:
Did the rapid inflationary expansion slow down a lot because the inflaton field had decayed, or because gravity from matter/radiation gradually decelerated the rapid expansion?
Inflation slows down and stops because the inflaton field decays.
In other words, did inflationary expansion instantaneously turn into non-inflationary because inflaton field had decayed, or did inflationary expansion gradually decelerate to be non-inflationary because of gravity from matter/radiation?
Neither. Inflation gradually turns into non-inflationary expansion because the inflaton field decays. Nothing happens instantaneously in this process.