  Transitional millisecond pulsars (tMSPs) have emerged in the last decade as a
unique class of neutron stars at the crossroads between accretion- and
rotation-powered phenomena. In their (sub-luminous) accretion disk state, with
X-ray luminosities of order $10^{33}-10^{34}$ erg s$^{-1}$, they switch rapidly
between two distinct X-ray modes: the disk-high (DH) and disk-low (DL) states.
We present a systematic XMM-Newton 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 $\dot{M}\simeq10^{13}-5\times10^{14}$ g
s$^{-1}$ and a viscosity parameter $\alpha\gtrsim$0.2.
