Yup, probably stretched cables. I usually tweak the cable tension every week after installing new cables until they stop stretching. Usually takes about three times to get it set and should stay that way for months or years.

Be sure the downtube lever for the rear shift is set appropriately for Suntour and compatible freewheels (including the SunRace 13-25 and 13-28). There's an alternate index shifter setting, just past the friction mode setting, but it's not for standard Suntour Alpha or SunRace freewheels. It'll shift to some gears in that alternate position, but it won't shift across the entire freewheel.

Refer back to that set of instructions I PM'd to you a couplafew weeks ago, for adjusting the rear derailleur. The limit screws are critical -- you don't want the RD to shift past the smallest or largest cogs, which could be disastrous. Then tweak the indexing.

While it can help to make basic adjustments on a work stand, I usually find it's necessary to ride the bike for finishing touches to shifting. Or check the bike on a resistance trainer like a Cycleops -- it mimics road riding pretty well and can help iron out shifting glitches.

On adjustment rides I'll keep a multitool in my jersey pocket or seat bag. Sometimes I'll tote a couple of Allen wrenches with longer shafts, since some multitools are so short it's a hassle to reach some adjustments.