Time-delay cosmography in strongly lensed quasars offer an independent way of measuring the Hubble constant, $H_0$. However, it has been proposed that the combination of microlensing and source-size effects, also known as microlensing time delay can potentially increase the uncertainty in time-delay measurements as well as lead to a biased time delay. In this work, we first investigate how microlensing time delay changes with assumptions on the initial mass function (IMF) and find that the more massive microlenses produce the sharper distributions of microlensing time delays. We also find that the IMF has modest effect on the the magnification probability distributions. Second, we present a new method to measure the color-dependent source size in lensed quasars using the microlensing time delays inferred from multi-band light curves. In practice the relevant observable is the differential microlensing time delays between different bands. We show from simulation using the facility as Vera C. Rubin Observatory that if this differential time delay between bands can be measured with a precision of $0.1$ days in any given lensed image, the disk size can be recovered to within a factor of $2$. If four lensed images are used, our method is able to achieve an unbiased source measurement within error of the order of $20%$, which is comparable with other techniques.
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