Unlikely there would be adequate Chloramine residual to eliminate the algae with only one regeneration cycle. If the reduction filter does not require backwashing for some time, perhaps the weak chloramine sitting in the line for an extended period will be somewhat effective.
Temporarily removing the affected section and circulating a strong bleach solution through it I expect would address the issue at least temporarily if the tubing is to continue to remain within the sunlight.
I would be inclined to replace the clear tubing with something opaque such as Black poly pipe.
Since the drain tubing is directly attached to water treatment devices that condition potable water, steps should be taken to keep the drain line clean and occasionally sanitized to prevent possible contamination of potable water flowing to your fixtures.
