Tariffs and internal improvements were planks leftover from the Whig party, which was national.There were numerous policy differences between the Republican Party and the Democrats in the South. As you mentioned, the Republicans opposed the extension of slavery into the territories which the south disagreed with. Furthermore, as part of their party platform, the Republicans in 1860 also advocated tariffs to protect domestic industry from foreign competition. Most of the manufacturing sector was located in the north and the southern states were opposed to such tariffs which would increase the cost of imported goods. The Republicans also wanted to pass a Homestead Bill in order to encourage the settlement of farms in the western region by offering cheap land in small parcels. Southerners feared that such a policy would discourage the establishment of large scale plantation agriculture. The Republicans also favored internal improvements to support the development of transportation facilities. Southerners viewed federal subsidies for such projects primarily as a benefit to the northern states which had a more developed transportation network. These are just a few examples of why the Republican Party was considered to be anti-southern.
"Large-scale plantation agriculture" = slavery.