There are some posts of a character presenting as masculine female but is trans male in lore. I'm wondering if I can add the tag 'tomboy' to some of these, even if it's technically untrue. First of all, many of these posts are already tagged with 'female' anyway, and I think someone searching the tomboy tag would prefer for them to show up, because it appears to be true out-of-context.
Examples:
https://e621.net/posts/1779452
https://e621.net/posts/1943673
https://e621.net/posts/578186
https://e621.net/posts/1457404
https://e621.net/posts/1748129

The short answer is Tag What You See. Other than lore tags, and to a certain extent character name, for a tag to be valid to a post it must be apparent in the post without needing any other context.

The longer answer is that the gender flowchart is to be applied first, based on the character's visible anatomical sex. Then if the character's gender identity is different, the trans_(lore) and appropriate gender identity lore tags are to be applied. And that's why Natani is tagged female even if that doesn't match his identity (although tagging Natani trans_man_(lore) is a whole can of worms, just to warn you).

For tomboy it requires the particular image being tagged to show "A female bodied character who has a stereotypically masculine personality (i.e. aggressive and brash) and/or style of dress." If those conditions aren't met then the tomboy tag is invalid regardless of whether the character is a tomboy in canon or other posts. For the images you've linked as examples the gym ones would fit tomboy IMO because Natani's gym wear is masculine styled and the breasts are either minimized by the binders or an attempt is made to ignore them. The tank image probably qualifies too because mechanic work is generally considered a masculine profession and Natani isn't doing some extra sexy/feminized "wrench wench" pose. The beach one falls just short of tomboy IMO because the binders aren't that different from a bandeau bikini and I don't think using magic to cheat at volleyball is distinctly masculine (although I suppose it could be argued to be "agressive and brash"). In he bridal carry image Natani's gender is ambiguous so tomboy doesn't apply since there isn't an apparent female bodied character to apply it to.

As a counter example post #1268691 absolutely should not get the tomboy tag because there is nothing in that post to indicate Natani acts like a tomboy in the larger context. If someone who searches the tomboy tag is interested in a character they find (eg Natani) and want to see more posts of that character, they can use the tag for that character; however if someone is looking for images of tomboys it clutters the search to have images of characters who sometimes act as tomboys, but aren't demonstrating that in every image with the tag.