Your contractor is full of ****. If you have it now, you will continue to have it. I have a sidewalk from the house to the garage. Down at the garage where is comes to the apron, the sidewalk will rise an inch depending on how cold the winter gets. If you have a mild winter, you may not get a lot of rise out of it. If you have a varying winter where it gets cold, then warm, then cold again, or just a super cold winter that is constantly cold, the frost will heave the concrete.
I was going to pin the sidewalk to the apron, but forgot, so it heaves there every year. The rest of the sidewalk, I had the gravel down for almost 2 years before I poured the concrete, so with the mower, roller, and whatever else running across it for that length of time, it was packed super tight. On a sidewalk, I always run two rows of rebar down the sidewalk, and I make sure that where the control joints are going to be at, the rebar is doubles up and tiewrapped together. That way the control joint will not crack and create a trip hazard.
It's hard to eliminate frost heave unless, you have a lot of stone underneath to absorb the moisture. If it is just concrete on the ground, you will have frost heave. Gravel gives room for the moisture when it freezes and fills the voids instead of wanting to push everything up.
How much gravel did he put down, if any?