is a very different series from Doctor Who
, aimed at a very different audience. DW is a family show, written with young viewers in mind but also enjoyable by their parents. TW is a "post-watershed" show (i.e. for airing after the kids have gone to bed) with lots of darkness, violence, profanity, nudity (almost entirely male), and heavy sexual themes. So undoubtedly its makers assumed that a lot of their target audience would not be Doctor Who
viewers. Any DW references are kept subtle and vague, just part of the general mysteriousness of the lead character's past. There are elements of the two shows that cross over and fit together if you watch them both in the right order, but that's a bonus; you can follow either one without needing to have seen the other. Indeed, if you're a fan of one, you might not be a fan of the other, since they're aimed at such different age groups and demographics.
Indeed, in some ways the two shows don't really fit together despite allegedly being in the same reality. For instance, there are a couple of episodes of TW involving things that are frankly supernatural, while in DW, everything that appears supernatural is explained in terms of aliens or superadvanced science.