Sufficiently fast continuous measurements of the position of an oscillator approach measurements projective on position eigenstates. We evidence the transition into the projective regime for a spin oscillator within an ensemble of 2 × 10¹⁰ room-temperature atoms by observing correlations between the quadratures of the meter light field. These correlations squeeze the fluctuations of one light quadrature below the vacuum level. When the measurement is slower than the oscillation, we generate 11.5_−1.5^+2.5dB and detect 8.5_−0.1^+0.1dB of squeezing in a tunable band that is a fraction of the resonance frequency. When the measurement is as fast as the oscillation, we detect 4.7 dB of squeezing that spans more than one decade of frequencies below the resonance. Our results demonstrate a new regime of continuous quantum measurements on material oscillators, and set a new benchmark for the performance of a linear quantum sensor.