The reasoning is this:
slave camps provide their flat bonusses by increasing population (they get+pop form adjacencies!). Slave research is based on the +1 the native building has, which is not unique.
If you are still hurting for production, try asteroid mines

. Just do it.
Yes - Work Camps once built after researching the 2nd "Colonization" Tree choice do currently increase population +1 per work camp and that +1 Population Cap bonus currently carries forward to the upgraded manufacturing bonus buildings for Slavers. Currently that makes Slavers ramp up production relatively fast. Note that prior to Crusade Population had a lesser role in influencing Raw Production for the planet than it does now. That said I have asked if Work Camps should increase Food Income instead of Population so you don't get the increased Raw Production without the additional step of adding Cities to the planet. Right now the Food Income for Colony Worlds without Farms is 4 Population giving a Slaver with 4 of more work camps a significant immediate Raw Production bonus and maybe this is okay but it has more drastic effect in Crusade it seems to me than it did before. So perhaps you don't need the Space Elevator Building (colony unique that as of 2.14 adds +1 MaxManufacturing) for Slaver's if that Population Cap bonus stays. Which similarly affects whether you get the Space Port (+1 Military Production) building for Slavers. But work camp bonuses can't be built immediately. Slavers as well as Non-Slavers can built the Deep Core Mine (Colony Unique not on the Homeworlds) building that adds +1 Social Manufacturing to the planet (perhaps this building should be restricted from slavers if they continue to get the +1 Population Cap from work camps).
Synthetics get a YorResourceExtractor colony unique building that adds +2 MaxManufacturing to its planet so surely they don't need all three of those buildings (Space Elevator, Space Port and Deep Core Mine).
Should Synthetics be restriction from building the Deep Core Mine (Colony Unique not on the Homeworlds) building that adds +1 MaxManufacturing to the planet) ??
Asteroid Mining now costs 100 manufacturing instead of 500 before Crusade and adds +1 Raw Production to the associated Planet (although I think there is some distance effect to that bonus). With a base of 4 Raw Production from population on any planet, Asteroid mines add a good bonus of production to any planet.
Also Yes - the Slaver Research Chambers (which should also be available only after Resource Exploration Tech is researched not available under Colonization) continue to have a +1 Research bonus per building that other Race's research buildings don't have as well as a Percentage Research bonus everyone has. With Lower Research percentage bonuses (about one third of the old bonus values) this bonus is more significant in Crusade that it was before. So perhaps you don't need a empire unique Computer Core building up front as a slaver but it does boost your initial research output.
Not sure how intentional this is but Synthetics can build immediately a YorMainframe building (+1 Research - planetary unique building) on all planets instead of getting a empire unique Computer Core building.
Computer Core building is empire unique and can be built immediately to give +2 research to the planet and currently is not available to Slaves or Synthetics.
Carrying these restrictions forward - the Central Bank building (empire unique like Computer Core) can not be built currently by Slavers or Synthetics. Not sure why since they have not direct replacement for this building which currently as of 2.13 gives 100% Gross Income bonus (was +2 gross income) to its associated planet.
Now Synthetics do get a Rare Metal Extractor that gives +25 % Gross Income but it is researched later with the Planetary Resource Mining Tech (ResourceProcessingTech) and seems to be a Racial unique building to help increase income for Synthetics whom don't get automatic increases to Raw Production or Gross Income from "natural" population growth.