Animals remember temporal links between their actions and subsequent rewards. We previously discovered a synaptic mechanism underlying such reward learning in D1 receptor (D1R)-expressing spiny projection neurons (D1 SPN) of the striatum. Dopamine (DA) bursts promote dendritic spine enlargement in a time window of only a few seconds after paired pre- and post-synaptic spiking (pre-post pairing), which is termed as reinforcement plasticity (RP). The previous study has also identified underlying signaling pathways; however, it still remains unclear how the signaling dynamics results in RP. In the present study, we first developed a computational model of signaling dynamics of D1 SPNs. The D1 RP model successfully reproduced experimentally observed protein kinase A (PKA) activity, including its critical time window. In this model, adenylate cyclase type 1 (AC1) in the spines/thin dendrites played a pivotal role as a coincidence detector against pre-post pairing and DA burst. In particular, pre-post pairing (Ca2+ signal) stimulated AC1 with a delay, and the Ca2+-stimulated AC1 was activated by the DA burst for the asymmetric time window. Moreover, the smallness of the spines/thin dendrites is crucial to the short time window for the PKA activity. We then developed a RP model for D2 SPNs, which also predicted the critical time window for RP that depended on the timing of pre-post pairing and phasic DA dip. AC1 worked for the coincidence detector in the D2 RP model as well. We further simulated the signaling pathway leading to Ca2+/calmodulin-dependent protein kinase II (CaMKII) activation and clarified the role of the downstream molecules of AC1 as the integrators that turn transient input signals into persistent spine enlargement. Finally, we discuss how such timing windows guide animals' reward learning.