Judging from what I heard in the audio samples and from various descriptions by native speakers, the situation looks like this:
This "weird" thing happens in the following contexts:
rd
rl
rn
rs
rt
This means that it's not really about the "t". What's interesting here is the behaviour of the "r".
Now my guess is: in such contexts where "r" is succeeded by a liquid (l, n), some fricatives (s), and plosives (d, t), it becomes rhotic. This means you've got a post-vocalic "r" in these situations (and when you look at words like "svart", "snart", "borta" etc. you'll know what post-vocalic means). Now, rhotacism is nothing unusual when it comes to Swedish - it is a rhotic language, just like German. Compare British RP, for instance, which is non-rhotic. American English, on the other hand, is rhotic.
Normally, you have a different sort of "r" in Swedish. Almost every language has its own "r", I suppose, and this is really a sound with many variants. Germans have the so-called "Zäpfchen-r" (it's formed somewhere near the gut), Scots have a lingual trill or a rolled "r"...and Swedish has a very rolled and fronted "r" as well (of course, there are regional variations). What happens in words with a "rd" "rl" "rn" "rs" "rt" combination is that the "r" assumes a somewhat different quality, probably in anticipation of the next sound (this is a common phonetic phenomenon). And out comes an "r" that's not unlike the (British) English "r" - it's formed more towards the middle of the mouth with the tip of the tongue curled...it's a very liquid sort of "r", i.e. no rolling or trilling. If someone attempted to speak British English (i.e. not pronouncing the "r" after vowels like in "card") but wasn't perfect at doing so, thus producing a slight reflex of an "r"...then you get what has been previously described as a "blend". Only that it probably isn't a blend because the "t" or whatever comes after is rather unaffected - it's the quality of the "r" that's different. The closest you can get to pronouncing words like "svart" etc. is to think of any English word like "hurt"...then trying to pronounce it somewhere in-between RP (without any trace of an "r") and, say, Irish English (which is a rhotic variety). The result should be somewhat similar to the way it sounds in Swedish.
That's just what I could gather from what I heard. No claim to correctness.
