Is there any way to make the output voltage waveform in-phase with my input in the emitter-follower circuit?
The TinkerCad scope traces show no indication of being phase matched. I suspect they both 'trigger' at the AC center of the waveform. Since the output waveform has its bottom half cut off, the scope trace is triggered half way up the positive half which makes it appear to have a phase lead. 

Try adding a DC bias voltage (lower knob) of about 8.2 V (15 V / 2 + 0.7 V) to the input signal. This should make the output a sine wave and the apparent phases similar. If it has the option of two traces on one scope then use that.