Cagayan is a mainly rural area with coastal towns and a population of just over one million people.
Aileen Torres, administrator of the Philippine National Red Cross (PNRC) in Cagayan, said her office was getting reports from volunteers that "chaos was all over" places across the path of the typhoon.
"The winds and rains are so strong. Power is out and we are relying on generators," she said.
Manila-based DZBB radio said heavy rains also pelted two towns in Zambales province north of Manila.
Its correspondent reported seeing flooding and some residents on the streets were holding on to trees so they would not be blown away.
Weather officials said Parma, packing winds of 175kph and gusts of up to 210kph, had veered away from the capital, Manila and nearby areas still reeling from the massive floods brought by Typhoon Ketsana last weekend.
|Ketsana left almost 300 people dead and affected about four million people [AFP]
While the capital was expected to be spared from Parma's powerful winds, it could still experience heavy rains that could worsen the squalid conditions in crowded evacuation camps and hamper relief efforts.
Gilbert Teodoro, the Philippines defence secretary, said: "While the storm has changed course, it does not mean there will be no rains ... We're not yet sure if it will not rain and if it will not flood again."
Heavy rains drenched Manila on Friday night and Saturday morning, adding to the burden of the sprawling city of 12 million people that was awash with flooding six-metres high last Saturday.
Ketsana's floods - the worst in 40 years in the capital - left 293 people dead and nearly half a million people displaced.
Florante Cruz, a tricycle driver, said he was relieved that the storm has spared Manila from its strong winds but was still wary of the rains.
"I heard it has changed course but we cannot be so sure yet.
"If it came here, my house would have been blown away," he said of his shanty in the middle of a flooded field.
After being accused of not preparing the nation properly for Ketsana, Gloria Macapagal Arroyo, the Philippines president, on Friday placed the Philippines under a "state of calamity" to expedite relief efforts and get ready for Parma.