As a dev/designer business owner, do your partners try to “manage” you?

You are either a co-founder or an employee, and if you are a co-founder acting like an employee you are at fault as much as the other co-founder(s).

If you are a co-founder then you should be in strategy meetings and helping to set direction. Just because you are the technical person doesn't mean you are excluded, in fact you are critical to those meetings. Any person who tells you otherwise is not being honest and doesn't have the company or your best interest in mind. It frustrates me to no end when I hear a founder say to a technical leader or other co-founder that they are more needed writing some arbitrary piece of code than in a strategy meeting where product, company or client decisions are being made. A single decision made in a meeting excluding the technical leadership can lead to chaos and cause friction where none need be, not to mention waste more time correcting then even a 1-2 hour long meeting. Excluding decision makers and leadership is always a mistake when strategy is involved. There are however plenty of sales & marketing meetings and others that you as a technical leader/founder do not need to be in, just as a business focused co-founder doesn't need to be in the technical detail meetings where you are working through implementation details of a defined feature (as an example).

To answer your question, there is a difference between co-founders holding you accountable and them "managing" you. Co-founders should hold each other accountable, but to daily manage you is not common, with some exceptions. That said, if you are the kind of person that needs daily oversight to stay on track it happens and I've seen it a few times, some people know themselves and ask a co-founder/friend for it. Also, if you are not really a co-founder but just an early employee with some stock/options then you are just an employee and will have more management. Each co-founder should also have a defined role (in addition to the 10 others they wear early on), so one will be CEO, and one might be CTO etc. With those roles that means people will have specific duties too fulfill and so there is an acceptance to those roles and responsibilities when you are growing a company.

Don't let a non-technical founder take advantage of you. A good litmus test is if the non-technical founder has anything to do on a daily basis. If it seems like there's nothing for them to do, because "it's too early," or "the product isn't ready yet," they're probably taking advantage of you. At that point, unless they've got money to offer (and preferably pay you), there is little reason for them to have the same level of equity as you, and you should ask yourself what you're getting from the relationship.