Assuming that the straight red and blue lines are your 30 degree markers... I've made some notes. Please take with pinch of salt and don't hesitate to point out any inaccuracies.
Think of your southern region of interest as India and the far east, your northern area of interest as Europe and Scandinavia (with some adjustments).
You have a strong circumpolar antarctic current in the south. Cold water currents flowing without hitting landmass. This is similar to real-life so you can use, South America, South Africa, Australia and New Zealand as examples of how cureents will flow.
Your southern right hand yellow area in question has no real connection to cold water sources. So your cold currents in it make no real sense, regardless of "rule" that they should...they still need a cold source. I believe it will be a slowish warm current gyre, circulating the water trapped in the area by the landmasses. The main entry/exit point for fresh water will be in the southwest, where water from the cold current hitting the western edge of your southern continent with flow northwards (similar to the Peru and w. Australian currents). Some water may escape through the eastern straits. Think warm waters interchanging through the Malacca Strait, Sunda Strait and Timor Sea etc.
Your northern left hand yellow area in question is trickier. You should also have a circumpolar current in the north (earth doesnt have this so it's not directly relatable). Cold water will be flowing east to west, reflecting off landmasses on the eastern edges, it doesn't have as much space to spread out so will probably not be as established and strong as the southern current. You should also have a warm current flowing northwards from your right hand side of the map (far east equavilant) towards your left hand side of the map. This warm current doesn't look to be very strong so it won't act in a similar manner to the Kuroshio or Gulf stream currents.
The Kuroshio, I'm not too familiar with, but it has a long fetch and carries alot of moisture that hits the cold n. american landmass bringing snow and lots of rain. The gulf stream brings warm water and air alot further north than would be expected bringing more temperate climates to Europe than would otherwise be expected.
Depending on the strength of your equavilent warm north current, you can either have something similar to what I drawn below (I'm not confident about it being so cold), or you can have a stronger warm current that hits the western edge of your northern islands and flows back south, similar to the gulf stream dynamics although not as strong. This would probably still have some input from the cold current. And would still be fairly cool when flowing south just below your circled area.
Orange are warm surface currents and green are cold surface currents.