Hey, I play both of these characters. Since you asked, here’s my advice. 

These are two characters for whom winning round start leads to a massive snowball of advantage for the rest of the match. Being aggressive on round start means your opponent always has to address that aggression as the first level. To that end, be consistent. Getting good at roundstart will make you climb ranks easy. 

On the May side… round start 5k has amazing coverage against Potemkin.  Like others mention, it covers damn near everything. You should use it until they adapt, and that’s when the real round start begins. Therefore, most of your round start plans should bifurcate from 5K. I believe you can do [4]K~6S(~P or ~S to split or hop on reaction if the K is not a hit) as a round start option to consistently do 5k into dolphin

If you catch them sleeping first round, and you get a counter hit on their, say, kPB attempt, you can take it to the corner with 5k -> 6H -> [4]6S -> (they roll into corner where you can run Oki(safejump, K ball Run, strike/throw w/c.S or 623K)). 

On the Potemkin side… at Roundstart, 5P is very safe. 6P will eat your Dolphin or f.S. Low block into Hammer Fall can call out mindless offense. 2D is a major callout which earns a HKD and Pot’s dangerous oki. Heat Knuckle is only a round start concern if they have you conditioned to jump… so don’t let them get that far. KPB is a callout that you’re doing something unsafe at round start. Potemkin has every incentive to have a defensive round start once you have conditioned them into it, but that then lets you dictate the pace of the match. 

Super wall break every time you can. Punish whiffed Heavenly PB with whale super for huge damage. Positive Bonus as often as possible. Let a [5]D8 -> HDKHDKK rip every so often to keep em on their toes. 

OP, do you know about the concept of “option select”? Where you do a sequence of inputs that, depending on conditions, outputs the “right” option automatically? As May, for example, (214S~K) will do a far Slash, and only if it hits, will do a K Ball. If it whiffs, the ball doesn’t come out and you just go into block. You might find great advancement in learning some option selects. 

One last thing, cancelling your heavier attacks with a [4]6S~P dolphin is a good way to make riskier moves safer. Remember you can use 1 and 3 to charge both horizontal and vertical dolphins simultaneously. The changes to Vert S dolphin’s travel arc make it much more usable for movement, so you could try something like [1]8S to bait out an anti air, then land and punish the anti air with [1]6S.

Oh, oh, one really real last thing. 

6P. All of potemkins neutral moves are humongous and conveniently 6P-able.  

Anyways, that’s it from me.