Assessing the impact of mobility on epidemic spreading is of crucial importance for understanding the effect of policies like mass quarantines and selective reopenings. While many factors affect disease incidence at a local level, making it more or less homogeneous with respect to other areas, the importance of multi-seeding has often been overlooked. Multiseeding occurs when several independent (non-clustered) infected individuals arrive at a susceptible population. This can lead to independent outbreaks that spark from distinct areas of the local contact (social) network. Such mechanism has the potential to boost incidence, making control efforts and contact tracing less effective. Here, through a modeling approach we show that the effect produced by the number of initial infections is nonlinear on the incidence peak and peak time. When case importations are carried by mobility from an already infected area, this effect is further enhanced by the local demography and underlying mixing patterns: the impact of every seed is larger in smaller populations. Finally, both in the model simulations and the analysis, we show that a multi-seeding effect combined with mobility restrictions can explain the observed spatial heterogeneities in the first wave of COVID-19 incidence and mortality in five European countries. Our results allow us for identifying what we have called epidemic epicenter: an area that shapes incidence and mortality peaks in the entire country. The present work further clarifies the nonlinear effects that mobility can have on the evolution of an epidemic and highlight their relevance for epidemic control.