In radioactive emissions of beta particles (energetic electrons), a bound neutron in the nucleus changes into a proton inside the nucleus, with the emission of a electron and an anti-neutrino.
Since mass of a free neutron is more than that of a free proton, a free neutron also decays in a similar fashion, i.e into a proton, electron, and anti-neutrino.
A bound proton also changes into a neutron with the emission of a positron, and a neutrino. It needs to be emphasized that only a bound proton inside the nucleus, undergoes this conversion i.e. into a neutron, a positron, and a neutrino.
So although, electrons (positrons) are not present in the nucleus, these are spontaneously created at the time of decay and are emitted.
In beta minus (β-) decay, a neutron is converted to a proton and the process creates an electron and an electron antineutrino, while in beta plus (β+)decay ,a proton is converted to a neutron and the process creates a positron and an electron neutrino.
This does not mean that the nucleus contains electrons.