In many (not all, maybe not even most) churches in America have a ‘call’ during their service. This ‘call’ is for visitors to the church to come forward and be ‘saved’. Generally the visitors are not baptized on spot, just prayed over as they ask for Jesus’ forgiveness.  Also, some churches will have special services in addition to the regular weekly services. These involve large scale baptisms of new members and visitors.

So, spontaneous baptisms are actually quite common.