A strange card. Netrunner used to have currents, but these were banned because they could sometimes have too great of an ongoing impact and were hard for runners to consistently turn off. In terms of ongoing impact, this feels more like a current or an identity ability than an ice. It adds like $2-3 to the cost of the first run each turn (or gives the corp an extra 2 clicks of value plus a trigger for any identity ability that relies on installs). Depending on how the identity triggers work out, this feels like it would have been too much of an impact on the board state even as a current, and maybe it's too impactful to be an identity ability either.
I don't know 100% if this will get banned, but a cheap ice which punishes any turn a run is made on any server, that's going to squeeze out a lot of decks which are fun and deserve to exist.
Two kind things for Tributary: it's a Jinteki card which doesn't suck, and in particular positive-tempo Jinteki should be encouraged. And the counters to this card are kind of vaguely reasonable.