We consider a multi-source status update system consisting of two independent sources and one server. The packets of different sources are generated according to a Poisson process and served according to an exponentially distributed service time. We assume that the received status update packets need further processing before being used (hence, computation-intensive). This is mathematically modeled by introducing an additional server at the sink node. The sink server serves the packets according to an exponentially distributed service time. We derive the moment generating function (MGF) of the AoI of each source under a source-aware packet management policy. According to this policy, when a server (either the transmitter or sink server) is busy at the arrival of a packet, the packet currently under service is preempted only if the arriving packet is from the same source (hence, source-aware). Numerical results are provided to assess the results.