I would like to chime in here, as I have a little experience with licensing music for use on my website for my slideshow that displays when one first goes to my site.
Firstly, it is important to differentiate between music you have paid to be able to listen to, as opposed to music you have paid to use as part of a video or a web presentation. I have no knowledge of your situation Ben and do not intend to single anyone out here, but wanted to use this forum to make this distinction, as I have seen a number of users elsewhere who assumed that once they purchased a song to listen to they could also use it for other purposes. While in some cases that may be true, I don't think that is typically the case.
I pay yearly license fee for the usage of a very specific set of Amethystium music on my site. Through this arrangement I have developed a relationship with the composer that has been very fun and rewarding, and it feels good to support another artist in this way. I have recently been looking into licensing a couple other works from some other composers, but have not pulled the trigger yet.
The point being that if the origin site where you have gotten a specific piece of music from explicitly states it can be used for these type of projects then no worries, but unless it is explicitly stated I would not assume it is available for such usage without contacting the creator of the music first. You will almost always be greeted warmly as they definitely appreciate that you are recognizing their intellectual property and the hard work they put in to create their compositions. In many cases, license fees are quite different depending on whether the final product is for personal or commercial use (sometimes personal use can be free). Since I do sell a very small amount of my work, I have always endeavored to make that clear to the person who's work I am requesting to license.
Lastly, I always try to have an explicit attribution to the music creator along with the title of the track(s) I might be using, to give credit for that portion of my composite work to the appropriate person and to allow those who like the song(s) to go look up the composer, just like I would want done if someone was using one of my images in a presentation of theirs.
Hopefully I am not out of line here bringing this up, it just seemed like a good place to mention this aspect of adding music to one's videos or time-lapses...
ML