Sounds like either
a) Water stress or
b) Salt burn
The first thing to check is whether you have a salt build-up in the
soil--what color is the run-out if you water the plant so that water
drains freely from the pot? It should be colorless. You may need to
switch to distilled or deionized water.
>> I bought a Tea Tree (Melaleuca) about a month ago, it is currently about 2
> feet tall, it is alive and I have seen some new growth but all the tips of
> the leaves are dried out, almost burnt looking. Anyone have any ideas of
> what might be causing this. I water it about once per week when the soil
> seems to begin to dry, fertilizer was added when it was potted and again
> after about 30 days.