switching calibers, barrel break in?

[Noreaster]

I purchased a 40S&W barrel for my 357 sig. Swapped out the barrel and headed to the range. The new barrel would not group. I was horrified with the accuracy. Older gent beside me tells me it's ok, the barrel has to break in. A few mags later the gun actual shoots better and I can hold a decent group. Anyone else have this type of experience. How many rounds before it gets broken in?

[Hogtown]

swapped my sig 229 40 to 357, went straight to range, run 4, 12 round mags through it, mine shot great.