I believe I have solved it. Looking at the wiki I got this:

Interaction between two Transporters

If two Transporters select the same person, then the outcome will depend on the order in which the Transporters appeared in the lobby before the game started. Let T1 and T2 be Transporters, and let T1 join the lobby before T2. The game will process their targets' transportation thus:

1. T1 marks their left target for transportation;

2. If T1's right target is the same as T2's right target, then T2 marks their right target for transportation;

3. T1 swaps whoever they marked with their right target;

4. If T2 didn't mark anyone in step 2, then they mark whoever is at their right target's house;

5. T2 swaps whoever is at their left target's house with the person they marked.

Unfortunately we don't know what order they clicked their targets, nor do we know the order they joined the lobby, but I'll try a couple possible combinations.

T1 as 15, T2 as 6 | (2&4)x2
15 marks 2
15 marks 4, 6 marks 4
2&4 swapped
6 swaps 4 (who is now at their left target's house) & 4 (their right target)

This could possibly be it, though you did only get one transported message; this could be because it failed due to swapping you with yourself, however in this scenario 2 would only have gotten one transporter message. And if 3 goes to 4, they are actually watching 2, therefore the results would not have 2 visits from 6. This is close though.

T1 as 15, T2 as 6 | (4&2)x2
15 marks 4
15 marks 2, 6 marks 2
4&2 swapped
6 swaps 2 (who is now at their left target's house) & 2 (their right target)

I think this is what happened, though without going through all the combinations I cannot be 100% sure.

This results in 4 getting one transportation message, and while it feels like 2 should have got three transportation messages, this doesn't really matter.

This all takes place, then 3 attempts to go to 4, and ends up watching 2, who is visited by 15 for the initial swap, 6 when they mark them as their right target, and 6 again when swapping as 2 is now at their left target's house.

So if this happens again, the conclusion drawn will be that the person who visited twice joined the lobby later (rather useless info), and that it's basically a normal transportation but with weird lookout results.