Electrical – GFCI receptacle works partially when switch is turned off; not at all when on

I had an electrician install an outdoor receptacle recently, and it's not working as expected. Before the receptacle was installed, the only thing I'm aware of that was on this circuit was a single outdoor light fixture controlled by a switch. I swapped out the simple switch for a Honeywell RPLS540A (one of those no-neutral timer switches, as the switch box did not have a neutral available).

I was under the impression that the new receptacle was not hooked up downstream of the switch, and so it should operate at all times, independent of the switch.

Here's what actually happens (edited to reflect new information per DoxyLover's suggested diagnostic test):

• With the switch turned on, the receptacle is completely dead. The outdoor lights go on fully, but there are no signs of life at the receptacle. The green LED turns off, and nothing lights up on an outlet tester. The GFCI doesn't seem to be tripped here, as it doesn't actually need to be reset. If you turn the switch back off, the lights go off, and the receptacle goes to the state described below.
• With the switch turned off, the receptacle seems to get partial power and shows a dimly lit hot/neutral reverse with an outlet tester. The green LED light is on, and there is some power. Plugging in a 100-watt lamp, for example, results in partial power in the lamp plugged into the receptacle and partial power in the lights that are supposed to be switched off.

I'm confused as to why all this would be. It seems apparent that things are wired incorrectly, but what would cause this behavior? Part of what I'm after here is the issue of who screwed up: me in the installation of the switch or the electrician in the installation of the receptacle? (He should arguably have tested the receptacle a bit better, although I'd hardly rule out errors on my part.)

Second Update: I just went back to inspect my work in the timer switch, and it does appear to be installed according to the instructions given in the manual. Three wires come into the box: black (I assume line), white (I assume load), and a bare ground wire. The line and 3-way wires from the switch are wire-nutted to the black wire in the box, the load wire from the switch is wire-nutted to the white wire in the box, and the ground wire is wire-nutted to the bare wire. In other words, it's just like the diagram below (from the manual), except that the ground is connected to the bare wire instead of a screw in the box. I'm not 100% clear on how the receptacle is wired in relation to this.