My T has always asked me to call if I feel the need to self injure any time of the day or night (although I have never been able to do so yet, but that is down to my stuff /anxieties). Needing to SI is an awful place to be, really hard to resist the urges. I don't agree that we are supposed to cope in between sessions - we can't just turn on and off like that unless we're really good at disconnecting - I think the gap between sessions is there for us to learn to cope, but it takes a long time to be expert at that.
I pay my T for my sessions, but I also expect some availabilty between sessions as well - this is a tough journey for all of us and sometimes we need a little extra help.