Hey Lauren,
It sounds like those h1 tags are various page/site titles generated by your theme, do you agree? If not, can you provide more detail on what code your developer fixed, specifically, to address these problems?
Also, “problems” may not be the right word here – the suggestion of h1 tags on a page is just that: a suggestion. The report of those h1 tags not being there, then, is a diagnostic report and not so much an error like “without these h1 tags, your site will fail!”.
In fact, as long as your HTML document is valid in general, the biggest impacts on SEO are still just producing good content regularly, and not doing any sneaky / spammy tricks that engines like Google will penalize you for. If we use an h2 instead of h1, for example, then the impact of that is extremely negligible.
Just some thoughts there – not trying to minimize your concerns at all, just hoping to reduce some anxiety/urgency about this! Let me know what you think and share some more information about what changes your developer made, we can definitely keep the conversation going from there 🙂
Cheers!
George