Crossword Genius

Slowly drink last traces of advocaat then throw up on the rug (5)

Ross

I believe the answer is:

tapis

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'slowly drink last traces of advocaat then throw up' is the definition.
I can't tell whether this defines the answer.

'on the rug' is the wordplay.
'on' says to put letters next to each other.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'rug' becomes 'apis' (I can't explain this - if you can you should give a lot more credence to this answer).
't' put next to 'apis' is 'TAPIS'.

Can you help me to learn more?

(Other definitions for tapis that I've seen before include "Covering" , "Carpeting" .)

I've seen this clue in the Sydney Morning Herald.
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