I've found playing with a metronome or consistent click will improve your timing dramatically. Start out just playing straight 4/4 at around 120 Beats Per Minute (BPM) and once you're comfortable with it work some fills in paying attention to time. You may be surprised to find that you speed up or slow down coming out of the fill and you may have to work on some timing--or you may find that you have a great internal metronome and you're doing fine--either way you'll know what you do ad don't need to work on.
As for Thunder's comment, it is true that there are times when you play a bit behind the beat or
ahead of it depending on the pocket or the push you want to achieve in music, but you can usually find that better once you have established where the real click or time is. So, the metronome and click still benefit you in this situation as well.
Oh and if you can--wear headphones and get the click in there so you can hear it better otherwise you'll find yourself straining to hear it over your own drums or may not be able to hear it at all.... A strobe as you mentioned might help you to visualize the click if you can't hear it--- I dunno never used a strobe.
Most modern multi-track music is sequenced or the musicians were playing along with a click or sequence for synchronization of the tracks. Studio software like ProTools exists to make sure the time is accurate and they can even adjust timing, pitch, key, everything with the software after the fact if they need to fix it. Most recordings automatically are corrected for timing (quantized) so you can trust their meter to play along with.