No, you bought the right coils. According
to this page, the HW-M are suitable for Ello tanks. Those HW-M coils have a slightly different design (tapered sides) than the regular HW coils (straight sides) that come with your Pico 25/Ello but kit they're supposed to work all the same.
You problem is most likely that you didn't prime them enough. I saturate all my coils with ejuice before I close and fill the tank. I mean
saturate. Then I start them off at a really low wattage and work my way up little by little.
If that isn't the problem, then you may have gotten defective coils.
And in case you are interested in turning your Ello tank effectively into an RTA (you build your own coils,
please see my post here. This way, you can buy multiple RBAs, coil and wick them up ahead of time and carry them around with you in a baggie or whatever - just like you'd carry around factory coils. Saves you a lot of money. But that's assuming you are interested in single coil builds. Otherwise, not a good option.