It's not necessary, Adiamant...
It is not necessary to have the same speaker and subwoofer manufacturer as tonal and sonic characteristics as well as timbre matching have very little bearing on most frequencies handled by subwoofers (~120Hz and lower). On the contrary, you'll find that HT enthusiasts more often than not have a subwoofer/s from one company and their speakers from another.
The mains (front L & R) and center are the most critical speakers to have matching components as this is where the bulk of your soundstage is carried. Timbre matching is important for these three to allow for seamless panning of both soundtracks and music. If you're listening to multichannel (MC) music such as DVD-Audio or SACDs, the surrounds are also suggested to retain similar components as your front three speakers to again maintain the same tonal characteristics.
Having said this, the AS-P4000 is a decent sub for the money. If you have a smaller listening area (up to 2000 cu. ft.), it should do just fine. However, if you're using this in a mid-large to large listening room (2200 cu. ft. and up) and plan on listening at high volume levels (30db and lower), you may want to consider a more powerful sub. Keep in mind, the cost for said sub will also increase... -TD