Best way to connect microcontroller, sensor and LED
Aside from the "Sinking Capability" specification in the datasheet will be referring to the MCU operating as an output driving low [*], there doesn't appear to be anything immediately wrong with that circuit if you redraw it correctly.

By drawing it correctly I presume you meant to connect one LED/pull-down to each line - you have connected two to the same line and none to the bottom. As a side note, while the way you have drawn the wire connections is correctly to one of the two standards, it tends to be easier to use the dot-cross style (a dot shows wires connected, and if they cross over they are unconnected) as that means you don't have to draw the little arcs to jump wires over.

You will only get ~\$5\space\mathrm{mA}\$ flowing through the LEDs when the sensor is outputting high. If you want the 10mA you have written on your schematic you would need to decrease the resistor value to \$120\space\Omega\$.



[*] The inputs are typically "High Impedance" which means they will sink virtually no current.