Q:

Did the USS Olympia go forward in time?

DS9 "The Sound of her Voice":

LISA [OC]: My name's Lisa Cusak. Until a couple of days ago, I was the
  commanding officer of the Olympia. 
SISKO: The Olympia. 
LISA [OC]: We left the Federation over eight years ago for a long
  range exploration of the Beta Quadrant. 
SISKO: What happened to your ship, Captain? 
LISA [OC]: We were finally heading home, if you can believe that,
  then we picked up some strange energy readings in a nearby star
  system, and I decided to stop and investigate. We found an energy
  barrier around the fourth planet that was unlike anything we'd ever
  seen, and when we probed it with our scanners it triggered a quantum
  reaction. There was an enormous surge of metrion radiation that
  disabled our engines. The next thing I knew, we were spiraling in
  toward the surface. I gave the order to abandon ship and the last
  thing I remember is a console exploding in my face. I woke up in an
  escape pod on the surface and I've spent the last day and a half
  sitting in this cave trying to raise someone on subspace. 
BASHIR: Captain, Doctor Bashir, Chief Medical Officer. Your message
  said that you were on a L class planet. Are you sure? 
LISA [OC]: Positive. And to answer your next question, yes, I've been
  giving myself fifteen cc's of triox every four hours to compensate for
  the excess carbon dioxide in the atmosphere. Just like it says in my
  medical tricorder. 
BASHIR: How much triox do you have left? 
LISA [OC]: One hundred and fifty millilitres. 
BASHIR: Will you to decrease the dosage, Captain, to eight cc's every
  six hours. We need to stretch your supply as long as possible. 
KASIDY: What happens when she runs out of the drug? 
LISA [OC]: That's a good question, Doctor. What happens then? 
BASHIR: You will begin to experience the effects of hypoxia. But
  before that happens, the triox compound will have strengthened your
  cardiopulmonary system, allowing you to better withstand the effects. 
LISA [OC]: Better withstand the effects. In other words, I'm going to
  be gasping for air and turning different shades of blue by the time
  you get here.  
BASHIR: Yes, I'm afraid so. 
LISA [OC]: Thanks for brightening my day. 
KASIDY: Is there anything we can do? 
LISA [OC]: There is, actually. I can't sleep. I think the injections
  are keeping me awake and I haven't had anyone to talk to for two
  days.
SISKO: We'll be able to help you with that, Captain. I'll have one of
  my officers stay on the comm. line with you at all times.

So the ship left eight years ago, they were doing long range exploration, Lisa doesn't know anything about the Dominion war, and she's only been on the planet for two days. 
We learn later that the crew are communicating with her in the past, which is an entirely different issue.
Did the ship go forward in time when it hit the metreon radiation in the atmosphere? Is that the explanation that Lisa was giving? I'm confused about the time frame of how this all happened.

A:

The Metreon radiation caused a temporal lensing effect, sending her communications into her future (the Defiant's present), and their replies back in time (from their perspective) to Captain Cusak's present. There’s no indication that Cusak’s ship travelled in time; just the communications to and from it.
Dr. Bashir confirmed she had died 3 years and two months prior to them arriving at the planet in the Rutharian sector. So she would have left on her mission 8 years plus 3 years ago, making that 2363 (the episode takes place in 2374).
To put that into perspective, 2363 is one year prior to the first season of Star Trek: The Next Generation

