Droplet-wall impacts are well known to produce a wide variety of outcomes such as spreading, splashing, jetting, receding, and rebounding from hydrophobic and superhydrophobic surfaces. In this work, we focus on the growth of jets that form during the partial recoil of liquid droplets that impinge upon hydrophilic substrates composed of cylindrical micro-pillars of various dimensions and distributions (i.e., height, width, pillar spacing, etc.). Micro-pillars are fabricated on the hydrophilic silicon wafers by standard microfabrication processes, including metal etch mask patterning by photolithography, metal deposition, and lift-off to achieve the designed pillar shapes and spacing, and followed by dry etching for various pillar heights. Micrometer-sized drops of glycerol mixtures impacting micro-structured wafers are investigated using high-speed video photography. Impact velocities are varied to observe the influence of Weber number on the dynamic properties of the rebounding jet and jet initiation time, as well as whether or not the jet detaches ejecting satellite droplets normal to the substrate surface. The specific influence of the micro-patterned surfaces on maximum spreading, jet formation, jet tip velocity, and jet ejection is characterized. We find that the micro-patterned substrates have a significant effect on the behavior of the drop impact and jetting mechanism. From our experiments, we find that jet velocity is approximately 4 times that of the drop impact velocity. The jet formation time is shown to follow the capillary time scale as (ρDi3/σ)½ (where ρ, Di, and σ are density, initial droplet diameter, and surface tension, respectively).