First of all, your statement implies that volcanism didn't occur in Troodos. That is not true. Troodos was even referred to as "Troodos Volcano" once in Miyashiro's 1973 article about Troodos.
A geological map of Cyprus clearly shows that a large portion of the ophiolite is composed of lavas (volcanic) and dykes (sub-volcanic):
Note the red, brown and pink colors. This is however not the arc volcanism you were referring to but rather ocean floor volcanism in a spreading center setting.
As for your question, why there isn't any arc volcanism in Troodos, the answer is simply that it wasn't hot enough. Let's put the question of where the water comes from aside, and concentrate on what happens when water meets an ultramafic rock, which is what mantle rocks are.
You can see that serpentine is stable at temperatures lower than 600°C, and even lower at (the more relevant for our case) low pressures. At higher temperatures serpentine is not stable anymore and the stable mineral is olivine (a rock forming mineral in lherzolite and harzburgite). Olivine is a dry mineral, so what happens to all the water? The water acts to lower the temperature needed to melt the mantle rocks.
You can see the dry versus the wet solidus (the temperature in which a rock begins to melt) in the following diagram.
So to sum it up, serpentinite forms when water reacts with ultramafic rocks at low temperature, for example when seawater infiltrates the mantle rocks, or when fluids from the subducted dehydrated slab reach the colder shallow mantle rocks. Melting and consequently arc volcanism occurs for example when fluids from the subducted dehydrated slab rise to deep and hot mantle rocks and suppress the melting temperature to below the ambient temperature.
There are several reasons that the mantle rocks in Troodos were "cold" enough for this to occur. First of all, you are talking about very shallow rocks, very close to the plutonic section of the ophiolite.
You can see that shallow mantle rocks are in the 300-500°C range. The arc volcanoes that you see in that figure are situated above the areas where fluids from the subducting slab can infiltrate hot (1000ish°C) mantle rocks. So you can use the Japan Sea as an analogue for Troodos in this case. Now, it is true that temperatures were likely higher because magmatic activity did occur in Troodos, but as Troodos was a slow-spreading center, the magmatic activity was rather sporadic and localized. The Nuriel et al. (2009) paper that Lanzafame refers to actually advocates the idea that Troodos was a core-complex. That is, the mantle rocks were directly exposed to seawater due to faulting, which both cooled them considerably and facilitated serpentinization.
The Troodos ophiolite is indeed a supra-subduction zone ophiolite. And it is reasonable to think that arc volcanism occurred somewhere, but the record is absent from the Troodos ophiolite itself. If you are interested, look up "a h f robertson" on Google Scholar and read some of his newer work. The article you cited is from the 70s and much research has been conducted since then.