First of all, there is a difference between mAh and mA.
mAh is how many milliamps can be supplied over the course of an hour. For example, if your power bank was 1000mAh, then it could supply 1A for 1 hour, or 500mA for 2 hours, 250mA for 4 hours (so on and so forth). mA should be pretty self explanatory if you are using electronics.
I think you will need to check the specs of your project again, do you mean to say your project should consume 400-700mA? I am pretty sure you meant to say when your project was powered by the power bank, the power bank only delivered 150mA?
If it easily delivers 1.5A when your phone is connected, that shows it is not the power bank. It may well be your project that is not working correctly, or it quite simply doesn't require the power you seem to think.
I have had to make a few assumptions about your question in this answer, so if I have anything wrong, please write a comment, but I think what you really need to do is double check the specs on everything and provide the correct units as this will help make it slightly less confusing!