Discount table displaying conflicting rates of two rules

I currently only have the free version. If need be, I will upgrade, but the issue reported here should not be a matter of upgrading.
On a site currently under construction (not publicly accessible yet) I have two discount rules that can conflict: One Bulk Discount Rule for a select few products based on the number of these products to be purchased (set to apply if matched and ignore all other rules), and one Bulk Discount Rule based on the total number of items in the shopping Cart (NOT set to apply if matched and ignore all other rules).
When I go to the product page of any of the select few products that have product-specific discount rules, the discount table shown has the discount entries of BOTH discount rules on top of each other, rather than only the one that is supposed to overrule the other. I paste the table here. Note that the first set of discounts is for the Cart Bulk Discounts, which should not be displayed at all, while the second set exclusive for that product (starting after the line “31+ $4.50”) should be the one exclusively showing:

Range Price/#
2 – 2 $5.70
3 – 3 $5.52
4 – 4 $5.40
5 – 5 $5.28
6 – 7 $5.16
8 – 10 $5.04
11 – 15 $4.92
16 – 20 $4.80
21 – 30 $4.65
31 + $4.50
2 – 4 $4.50
5 – 9 $3.90
10 – 19 $3.30
20 + $3.00

When adding one (or more) of this discounted item to the cart, the system applies the correct discount of the second set (the product-specific one that is to overrule the Cart-wide discount), so the math is correct. Interestingly, if I visit that product’s page again with any number of items of it in the cart, the discount table is displayed correctly, with only the product-specific entries showing. If I remove that item completely from the Cart, the Cart-wide discount rows show up again.
If an upgrade to the PRO version is needed to prevent that flawed behavior, I will upgrade, but I’d like to be sure. Also, such a mistake should not be part of any version of the software. Unless, of course, it is some kink specific only to my install, at which point I wonder how to fix it…