The primary use for the well is to allow sorcerors to use sorcery on their clanmates. A ritual allows them to draw a sample of a specific vampire's vitae from the well, which may be used to affect them with sorcery from afar. It is believed ur-Shulgi used the Heartsblood as a focus for breaking the Tremere curse on the clan.
The vast majority of Assamites have contributed some vitae to the well, but some may never have done so. While it is said that it can be used to affect any Assamite, however, an Assamite that has never contributed vitae to the Heartsblood may be unaffected by magical effects used on the clan as a whole (assuming the Heartsblood was the focus for the effect). This may be why the various curses leveled against the clan have not always uniformly affected every Assamite... or been broken for everyone all at the same time.