Being on salary means that you're not paid for the number of hours you work. Instead, being on salary means that you're paid a fixed amount to be responsible for something.
Developers are generally salaried professionals because of the great deal of decision making involved in their career.
Thus, if a decision you've made results in a less-than-desirable result, like a valued client experiencing downtime, then yes, you may need to come in and fix the problem. If unforeseen circumstances cause your client downtime, then you may need to fix their problem.
In my opinion, the question isn't about being on-call vs not on call. It's about taking personal responsibility for meeting goals and doing whatever it takes to keep your customers happy. If your goal is to clock out at 5pm and forget everything, then perhaps a salaried software developer job isn't for you.
The question you need to ask yourself is how invested are you in your line of work, not whether or not you remember signing something. Additionally, salaried employees, at least in the United States, aren't subject to the same labor laws as hourly employees. Therefore, you may not be required to actually sign anything in order to work overtime or outside of normal business hours.
With that said, perhaps your employer should have set the right expectations at the time of hire so you would have had the opportunity to decline their offer of employment.
There are organizations that hire people and don't have business requirements that require on-call staff. You could seek employment for one of these businesses, as some people's personal lives do require a smaller commitment than others.