A recent investigation of the effect of different antiretroviral drug classes on first phase dynamics of HIV RNA plasma virus levels has indicated that drugs acting at stages closer to viral production, such as the integrase inhibitor raltegravir, can produce a steeper first phase decay slope that may not be due to drug efficacy. Moreover it was found that for most drug classes the first phase transitions from a faster (phase IA) to a slightly slower decay region (phase IB) before the start of the usual second phase. Neither of these effects has been explained to date. We use a mathematical model that incorporates the different stages of the HIV viral life cycle in CD4+ T cells: viral entry, reverse transcription, integration, and viral production, to investigate the intracellular HIV mechanisms responsible for these complex plasma virus decay dynamics. We find differences in the phase IA slope across drug classes arise from a higher death rate of cells when they enter the productively infected stage post-integration, with a half-life of approximately 8 hours in this stage, whereas cells in earlier stages of the infection cycle have half-lives similar to uninfected cells. This implies any immune clearance is predominantly limited to the productive infection stage. We also show that the slowing of phase IA to phase IB at day 2 to 4 of monotherapy, depending on drug class, is a result of new rounds of infection. The level at which this slowing occurs is a better indicator of drug efficacy than the slope of the initial decay.