You don't say where you are located or what the weather is.
Most manufacturers say on the label not to install at temps below 45 to 55°F. This is not only because the shingles might not seal but because they are more brittle at cold temps. Further, many manufacturers void warantees when installed over old shingles.

I have installed thousands of squares over old and in cold weather, one or the other. It can be done but only at risk.
On a smooth plywood surface, the shingles have backing to lay to as they warm up and will eventually seal but with the voids created under them by the old shingles, sometimes they never seal properly. It should normally take one day at high temps or a couple of weeks at moderate temps up to sixty. The other thing that can preent permanent sealing is if you live in a dry, dusty place like west Texas or Arizona and suffer dust storms before they seal. That powdery coating blown in under the shingles will prevent setting.

Sorry...I live in central Iowa and the weather is typically in the mid-upper 20's with occasional light, fluffy snow. Currently, the highs have been forcasted for the teens and lows in the sub-zero's, but this weekend we're due for some 30-40 degree weather. In the summer, we're usually in the 80's at the very least...will these shingles wait that long to properly seal?

I guess it's too late to do anything about this but take steps to ensure they seal properly when it warms up...any ideas? The underlying layer of shingles is still in decent condition and lay almost perfectly flat.