Aims: SYMPA is the first instrument dedicated to the observation of free oscillations of Jupiter. Its principles and theoretical performance have been presented in Paper I. This second paper describes the data processing method, the real instrumental performance and presents the first results of a Jovian observation run, lead in 2005 at Teide Observatory. Methods: SYMPA is a Fourier transform spectrometer which works at a fixed optical path difference. It produces Doppler shift maps of the observed object. The velocity amplitude of Jupiter's oscillations is expected to be below 60 cm s-1. Results: Despite light technical defects, the instrument was demonstrated to work correctly, being limited only by photon noise. A noise level of about 12 cm s-1 was reached on a 10-night observation run, with 21% duty cycle, which is 5 time better than similar previous observations. However, no signal from Jupiter is clearly highlighted.