Inter-core crosstalk is a potential limitation on the achievable data-rates in optical fiber transmission systems using multi-core fibers. Crosstalk arises from unwanted coupling between cores of a homogenous multi-core fiber and it's average power has been observed to vary over time by 10s of decibels, potentially requiring an additional performance margin to achieve acceptable outage probability. Most investigations of crosstalk have so far only considered continuous wave laser light or amplified spontaneous emission as sources of crosstalk. In this paper, we theoretically and experimentally investigate the time-dependence of inter-core crosstalk in a homogeneous multi-core fiber when considering signals with various modulation formats and symbol rates. We find that crosstalk power fluctuations depend on the symbol rate, modulation and skew between cores. For carrier-free signals, such as quadrature amplitude modulation, the crosstalk power is nearly constant for expected conditions of multi-core transmission systems. However, carrier-supported signals, such as OOK, always induce time-varying crosstalk powers.