No. In Starfinder, healing spells heal the undead in the same way as they heal regular living creatures.
Starfinder is based on Pathfinder. So let's first check the original Pathfinder rules first to see where it describes the way healing magic affects the undead.
One section which says that undead get hurt by healing magic is found in the Undead Trait which reads:
Undead creatures are damaged by positive energy, are healed by negative energy, and don't benefit from healing effects.
This rule is also found in the descriptions of the spells "Heal" and "Harm" which respectively read:
If the target is undead, you deal that amount of positive damage to it
and
If the target is a willing undead creature, you restore that amount of Hit Points.
Now let's check the closest equivalents to these articles in Starfinder and see what we find there regarding healing the undead.
Starfinder does not have an "undead trait". It only has a creature type graft named Undead, which references two traits "undead immunities" and "unliving".
"Undead immunities" contains nothing about healing. "Unliving" however says:
magic effects can heal undead.
The Starfinder equivalent to the "Heal" spell is the "Mystic Cure", which does mention undeads:
In addition to healing such a creature, the spell returns the target to life, and the target takes a temporary negative level for 24 hours. This spell can’t resuscitate creatures slain by death effects, creatures turned into undead, or creatures whose bodies were destroyed, significantly mutilated, disintegrated, and so on.
The word "rescuscitate" in this context apparently means that it can not "cure undeadness" by turning an undead back into its living form. But it does not say anywhere that undead creatures can't recover HP from mystic cure.
So not only are healing spells in Starfinder no longer harmful to undead. Undeads benefit from healing just like any other creature. And this appears to be an intentional rule change from Pathfinder. Otherwise they would not have had a reason to write that down explicitly in the description of the "Unliving" trait.
Why exactly they made that rule change is speculation. But I would assume it's because in DnD/Pathfinder, healing magic is thematically "holy" while necromancy is thematically "unholy". The way healing magic affects undead in DnD/Pathfinder represents this theme. But this whole divine morality theme does not really fit into the scifi scenario of Starfinder. So it was dropped, and with it the mechanics which represent it.