Overturning should be designed using the code load factors. There used to be a confusing legacy clause that also had an overturning factor of safety, but that's been removed to the best of my knowledge.
For most conventional structures, you'd be designing to something like the 1.4xWind + 0.9 Dead or the 1.0 EQ case. That incorporates overturning.
If you are just looking at overturning resistance and not bearing pressures or anything else, yes it should be okay to use the ULS loads and an additional factor of safety of 1 as long as the correct ULS load case is being used and you're reducing any other dead loads you're accounting for in a similar way (i.e. if you're determining a footing weight, make sure your only using 0.9 x that weight for resistance when you're using that load case)
There are multiple answers to what to do with overall footing design:
1. Technically the correct approach is to design everything using ULS including partial factors on the soil resistance values. There is documentation for this, but it's a bit of a dig to do it and there's still some stuff that gets a little awkward (moment resisting shallow footings for instance)
2. There's a fair amount of simplified ULS foundation stuff where you look at all the load cases and manufacture one or two governing cases that significantly envelope the design
3. It's still fairly common to do a working stress design for foundations even though the code doesn't allow for it
4. Some people envelope it and use allowable stresses on the soil side and factored loads, so you end up with an additional 1.5-ish factor of safety on things
I tend to do option 1 for deep foundations and for simple shallow foundations, and I do option 3 for anything shallow with a moderate overturning on the footing with some confirming ULS checks for documentation.
Regardless of the above, you need to at least do a two line check that overturning of the footing is consistent with the ULS load factors and make sure your strength design for the footing is ULS.
Also, be aware that if you're using the ULS loads as inputs for any sort of semi working stress design you still have to make sure you're using the right combination for the right check. Your bearing pressure check may be with 1.25D or 1.4D and your overturning with 0.9D, for instance.
