Echinotriton breed on land and lay eggs underneath the plants/moss/mulch on the banks of ponds (Xie, Fei, Ye, Cai, Wang and Sparreboom). The larvae enter the water on hatching, probably by being washed into the ponds.
All Tylototriton (the four familiar ones in captivity anyway - T. shanjing, T. verrucosus, T. kweichowensis and T. taliangensis) mate and lay eggs in water, though sometimes a few eggs may be laid above the water level (Fleck and others).
Echinotriton is a very terrestrial genus. Of the Tylototriton species, T. verrucosus can be kept almost completely aquatic during the warmer period of the year. I keep them fully aquatic all year round, but if the temperature drops below 18 degrees C they tend to prefer a semi-aquatic setup. Some people keep T. kweichowensis almost completely aquatic too, but it probably isn't as comfortable with this as T. verrucosus.
I'm not certain about T. taliangensis but I believe that some people keep that species in a relatively aquatic setup too. T. shanjing is probably the most terrestrial, but I think it's fair to say that any Tylototriton species may enter the water for an extended period of time during the breeding season, which is generally most of the late spring, summer and early autumn.
Here are some references for you:
Xie, F., L. Fei, C. Ye, C. Cai, Z. Wang and M. Sparreboom (2000). "Breeding migration and oviposition of the Chinhai Salamander, Echinotriton chinhaiensis (Caudata: Salamandridae)." Herpetological Journal, 10 (111-118).
These two articles are in the same edition of elaphe (a publication of the German DGHT):
Fleck, J (1999). Weitere Beobachtungen an den Gattungen Echinotriton/Tylototriton (Beiträge der DGHT-AG Urodela-Tagung 1998) [Further observations of the genera Echinotitron/Tylototriton (A contribution to the DGHT-AG Urodela conference 1998)], elaphe 7(2).
Sparreboom, M (1999). Haltung und Nachzucht von Tylototriton verrucosus [Husbandry and Reproduction of Tylototriton verrucosus], elaphe 7(2).