yes thats what they will answer you, however you can miss out on the spirits in tavern. i thought so too that it adds twice and then takes one off, but if you click fast enough after a card popped for the next time on refresh and you click it away too fast (while its blinking/adding up spirits) it doesnt add double the spirits and deducts you the same amount during spinning. i have confirmed this in the past with screenshots where i was able to hold the same spirit count after popping up 3 purples and golds in a row. all you need is auto and click fast enough.
to avoid this you can simply wait a couple seconds after popping a hero or like i do click on shuffle anyways but not claim the card if i dont need want/need it.

as far as coins/runes concern its absolutely right that you most likely lag and not have lost any coins. i couldnt prove it so far but i am suspecting its a small calculations error but so insignificant that you wont notice a difference. the closest i ever came to prove it was when i was stuck at the high keeper after a sync and it took away the last purple i got and added coins. then when i clicked on the rune keeper again it deducted coins, gave me a different purple and re-sync again. i was able to repeat that several times until i clicked on the stone, got some coins and was able to overcome the loop. point is, after it synced it should have the correct amount of coins and i should have been able to just continue or due to a lack of coins not at all.
i would like to emphasize the insignificance tho, we are talking about 1-2k at the most and not 3m+