So I have done some research on the topic, including reading what I have written myself about it here: https://www.sommarskog.se/bulkload.html#UTF8 :-)
BULK INSERT is not able to handle terminators outside the ASCII range when you have a UTF8 file. I have filed a bug for this that you can vote for: http://feedback.azure.com/forums/908035-sql-server/suggestions/32899759-bulk-insert-cannot-load-utf-8-files-with-a-non-asc
If you want to stick with BULK INSERT, you need to use a separator that is in the ASCII range.
If you want to use the Universal Currency Sign, you can load the file with BCP:
bcp Somedatabase.tmp_owner.tst_tbl in tst_tbl.txt -c -t"|" -r"¤\n" -S Server -T -F2 -C 65001
Note that the  before the ¤ is not a typo. You need to specify the separator as a byte sequence, so ¤ are not UTF-8 here, but Latin-1. Confusing, eh? (And to muddle the waters even more, \n actually stands for \r\n.)