Transitional millisecond pulsars (tMSPs) have emerged in the last decade as a unique class of neutron stars at the crossroads between accretionand rotationpowered phenomena. In their (sub-luminous) accretion disk state, with X-ray luminosities of order 10 − 10 erg s, they switch rapidly between two distinct X-ray modes: the disk-high (DH) and disk-low (DL) states. We present a systematic XMMNewton and Chandra analysis of the aperiodic X-ray variability of all three currently known tMSPs, with a main focus on their disk state and separating DH and DL modes. We report the discovery of flat-topped broadband noise in the DH state of two of them, with break frequencies of 2.8 mHz (PSR J1023+0038) and 0.86 mHz (M28-I). We argue that the lowest frequency variability is similar to that seen in disk-accreting X-ray binaries in the hard state, at typical luminosities at least 2 orders of magnitude higher than tMSPs. We find strong variability in the DH state around 1 Hz, not typical of hard state X-ray binaries, with fractional rms amplitudes close to 30%. We discuss our results and use them to constrain the properties of the accretion disk, assuming that the X-ray variability is produced by fluctuations in mass accretion rate, and that the break frequency corresponds to the viscous timescale at the inner edge of the disk. In this context, we find that the newly found break frequencies are broadly consistent with a disk truncated close to the light cylinder with Ṁ ≃ 10 − 5× 10 g s and a viscosity parameter α &0.2.