I have the system running from a small pump in a waterbut this means it does not require the adapter. however the pipes are difficult to get securely on the T piece and some plants get much more water so a semi flow restrictor made from a cable tie solves this. by using a pump the pressure has been increased and this has not affected any of the parts.
very useful pump to drive a 4mm irrigation system. set on a timer and with half power can water 12 pots. however water did have to be raised by over a meter, the pump could not do this so the water but was raised to 0.5m an now works very efficiently.