MKS Chaintug help

So, I got a pair of 8 mm MKS tugs. I thought it seemed very bulky on the track end in terms of width. In any case, the size meant that it interfered with the Phil Wood dome I have on there so I sold them on.

I then got a 5 mm MKs tug which fits perfectly well (BJ Vigorelli) and leaves room for the Dome (I know that with a tug the domes should not be needed - I might revert back to normal Phil Wood washers). This tug works really well and has already helped make the bike more the low-maintenance machine that I had hoped for.

Anyhoo - my problem is this. Does the washer part of the tug go inside or outside the dropout? The leaflet that came with the tugs (in Japanese) has diagrams that do not provide clues. Searching on here doesn't give any clear answers.
Advice appreciated: in or out?

I see that the thin MKS chaintug fits track ends up to 5 mm, according to Hujub. Is that an accurate upper limit? I measure my Bob Jackson's at 5.3 mm ish. The fat ones look a bit more bulky than I'd like.

Not that I like tugs much in any case, but just occasionally my wheel moves fractionally, no matter what I do.