Normal Practice To Use 6 1/2" Sub With 8" Speaker?

I have a PMC TLE1 subwoofer with dual 6 1/2" drivers and speakers with 8" drivers. I am thinking whether it is a norm to combine subwoofers with speakers that have bigger drivers. The PMC subwoofer with smaller drivers goes down flat to 22Hz while the speaker with bigger drivers goes down to 40Hz+/-3dB. I am just curious since my impression is it is more appropriate to use subwoofers with a driver size that is at least similar or larger than the speaker's driver apart from looking at the specifications.

In my case I reckon it is technically acceptable to hook up the sub to the speakers since it does go down lower than the speakers? I just feel a little awkward using a sub that has smaller drivers compared to the main speakers although the results can be good(I think).

Any advice would be appreciated.
In general, the larger the driver the less cone excursion is needed to achieve a given SPL. Extreme cone excursion, as is often the case with subwoofers, causes distortion. Small drivers can play low, just not loud. With the combo you describe the 8" drivers may need to be "loafing", but that ain't a bad thing.
Measure the response in your room with and without the TLE1 and you'll know immediately.