@givemersspls
Testing Satsuki was part of being possessive, especially given the fact that she knew Satsuki was leaving, its the same with letting Watari go. If she actually trust him she wouldn't say what she did or send the pic, because then he'd just be seeing off a childhood friend. She had to tell him and Satsuki pretty much knew that, because Ishihara is obsessed with being a 'good girl' and a 'good girlfriend' and a good girlfriend wouldn't keep that from her boyfriend. Satsuki gave her an impossible choice so she took action to uphold her image while holding on to Watari.
You have to remember that she came over to feed Satsuki and not Watari, using
his favourite dishes when sending off her has meaning.
As I said, nothing is super bad, but your original comment of saying she wasn't being possessive was quite contrary to what was happening.