Sounds like you both have "wifi calling" turned on. That's a pretty valuable thing, in some situations, but the charges are not always zero. For you to have received a text "by wifi", Verizon had to know you were in Ireland (I guess wifi calling reports your position back to Verizon, which is kinda like roaming). Verizon then had to try to send the text via the internet over wifi. For wifi calling to work, it has to send data through the local wifi network, and then to the Verizon network. I guess that's the "data" they see.
As for charges, that's complicated. You have to look deep into your plan's details, regarding "Roaming", and "International Roaming". If you don't specifically turn off Roaming, then it seems Verizon figures you want to do International Roaming. If you don't have a plan add-on for International Roaming, I guess it gives you the $12/day option.
So for Verizon, you need to turn off "Roaming", and probably "wifi calling". AND read all the fine print.
For Tmobile, it's similar. My Tmobile plan includes International Roaming in 200+ countries, with some data limitations, and some charges for texts and calls. I think International calls are 25 cents/minute. BUT, earlier this year, I called an Irish hotel twice, total of 26 minutes. My big mistake was having "wifi calling" on, and I had forgotten that international wifi calling was 3 Dollars/minute. So I got a $80+ addition to my monthly bill.
Bottom line, wifi calling is not always free. It does not work without the use of your cell network in the U.S, and a foreign network in Ireland. So some cell companies have charges.