It's fine for a couple to create parameters around their relationship about what is acceptable or not - whether or not they are monogamous or in some type of CNM relationship. The problem (for anyone and everyone) is when one partner begins to create new rules and tries to unilaterally impose them on the other person.

If you don't feel confident in your partner's fidelity and you think the solution to that is to monitor their phone, make them check in at regular intervals, etc. you need to break up. If both partners don't operate out of a place of affection and trust, if both partners don't relate to each other as mature adults - then they have no business being together.