Thank you for reaching out. I tested this for you and was able to replicate the issue you described—on my laptop computer the "Add to cart" button shows, but on my Apple mobile device the "Buy it now" option displays. I believe this may be in relation to dynamic checkout buttons, which are influenced by the type of device the customer accesses the store with. You can try disabling them in your theme as per the instructions here.
If you still experience the same issue after disabling the dynamic checkout buttons, please let me know.
Victor | Shopify Social Care