Accurate cell detection in time-lapse microscopy is essential for quantitative cell-based assays but remains challenging in settings with limited labeled data and time-varying image acquisition conditions. These challenges are particularly pronounced in perfusion-less lab-on-CMOS platforms, where long-duration bright-field imaging is used to establish ground truth for label-free electrical measurements and where experiment-specific artifacts such as focus drift induce domain shifts across time points. In this work, we formulate cell detection for lab-on-CMOS time-lapse microscopy as a transductive learning problem in which unlabeled target images of interest are available during training. We propose a two-stage transductive correlation-filter-based detection framework with pseudo-label adaptation. A source-domain correlation filter trained from a small labeled set is first used to generate region proposals on a target image, and high-confidence responses are treated as pseudo-labels to train an imagespecific correlation filter for refined classification. Experimental results in a lab-on-CMOS time-lapse dataset achieve AP50 scores of up to 0.87 and consistently outperform inductive baselines and classical correlation-based trackers that experience domain shift. These results demonstrate an annotation-efficient and scalable detection strategy tailored to lab-on-CMOS time-lapse microscopy.