My understanding is the volume that is compost will eventually become negligible as it breaks down. I'm not sure how long that would take, but I'd think you need to overfill the low spots if you include much compost in the mix.

A big part of the problem was probably the tilling. When a lawn is tilled, it often settles unevenly and you get a lot of bumps.

As Anubis said. compost will continue to break down, so if there's a lot of compost, you'll get further settling.

Compost would help with the drainage issue, but you'll need to reapply it (or some other organic amendment) on a regular basis to get the soil draining well.

The proper way to fill in low spots in a lawn is to make a large X in the depression, roll back the sod, and fill in to just above the surrounding soil level (to allow for settling). For high spots you do the reverse, make that X, roll back the sod, and remove enough soil to get the sod level with the rest of the lawn.
If you simply put sand, topsoil, compost into the depression to raise it up you can cover the grass plants crown, where the growth comes from, and kill that. If you do not put down more that about 1/2 inch at any time and allow the grass to grow back it can take years to get the level up to where it should be.