I had one transaction to Bangkok bank not coded as international. I went to Kasikorn (Wise's partner in Thailand, and the bank the transaction came through on the way to Bangkok bank) and got a letter verifying that it was an international transaction.
But immigration never noticed it wasn't coded as international. In the 3 years I've been transferring money in every month, that's only happened once.
And as stated, use the 'funds for long term stay' reason in the drop-down.
In terms of transfer times, Wise does not take money from your home country bank account and transfer it to Thailand. Instead, it finds local, matching transactions in the two countries, and matches them up. This process takes longer. In general, the larger the amount, the longer it takes.