I'm going to suggest that you are watering too frequently. Nutgrass, or nutsedge, is a swamp grass that is perfectly happy growing in a stream. Having said that there is a look alike weed called green kyllinga. The main visible difference is the way the seed heads look. The big practical difference is that green kyllinga is not a swamp plant and is happy with no supplemental water period, ever. The good(ish) news for that is that green kyllinga is not nearly as invasive as nutgrass. I had nutgrass get started in my yard in San Antonio. Because of the way I water (deep and infrequent) it would go away...until the next 4-day rain event dropped 3-4 or more inches of rain. Then the nutgrass would return.

There are getting to be more and more herbicides that will kill nutgrass. The two originals are Image and Sedgehammer. There are people here with more better experience who will see the title and give you better herbicide info. Since I don't use it I can't get that deep into the details for a good, modern, sedge herbicide.

Nutsedge thrives in high moisture, sprinkler, hose or rain. The sedge killer formulation is expensive but it works. Make sure it says it kills nutsedge. nutsedge wiil rear its ugly head every time there’s a high moisture situation. IOW, you rarely get rid of it completely, more like control it.

Once a week is likely too frequent and 10 minutes is likely not long enough.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

depends on your grass though

Not so much. Grass type is one factor along with mowing height, cloudiness, humidity, wind, soil type, and some others that don't come to mind right now. When all is said and done, if you go by air temperature you will be pretty close.

Sulfentrazone is the active ingredient you want, I like sedge ender but sedgehammer & ortho nutsedge killer both work great

RoundUp for Lawns also has sulfentrazone in it, so there's another option.

Check the label on that round up for lawns first, Bermuda will not respond well to the 2,4D that is in most of those formulations

Yep, there's two formulations of Roundup for Lawns, one for cool season one for warm season. You'd want to make sure you get the right one.